Since such generic models are complex it is natural that these initial endeavours that attempt to quantitatively explain the temporal features, include stochastic propagation in an approximate manner where it is assumed that the accretion rate varies at different radii and that the time taken for the propagation to move inwards is the local viscous time-scale. On the other hand, there are approximate analytical techniques which have been used to describe the diffusion process in the accretion flow and quantify the basic prediction of the propagating fluctuations [1]}, [2]}, [3]}, [4]}. For example, while [3]} describes the propagation in terms of cylindrical sound waves, [4]} have used the approximate Green's function formalism of [1]} and [2]}. Solving the disc equations in a linearized form [9]} have shown that any transition radius in the disc will act like a low-pass filter to such fluctuations and have argued that resonant features may cause Quasi-periodic behaviour. It is possible, however, to solve the time dependent hydro-dynamical equations with a stochastic viscosity to obtain the full global non-linear behaviour of the disc. [10]} simulated such a disc with global stochastic fluctuations in the viscosity and confirmed the non-linear behaviour of the \(r.m.s\)  being proportional to the flux. They found that the accretion rate variations at frequencies lower than the local viscous frequency is coherent for different radii and hence revealing the basic idea of propagation fluctuation. They computed the expected time-lags and found that their magnitudes are smaller than the viscous time-scale and that they are frequency dependent. Further, [11]} performed global magneto-hydrodynamic simulation of accretion disc and confirmed that the Maxwell stresses in the low frequency regime, indeed produce fluctuations which propagate inwards. These simulation results, especially that the time-lags are a function of frequency need to be incorporated into future models which would strive to quantitatively explain the temporal behaviour of accreting systems.
